Asymptotes and Holes of Rational Functions

Find the vertical asymptote(s), hole(s) and horizontal asymptote.

• V.A.: x = -1
  Holes: x = 2
  H.A.: None

• V.A.: x = 2
  Holes: x = 1
  H.A.: None

• V.A.: x = -1
  Holes: x = 2
  H.A.: y = 1/4

• V.A.: x = 2, -1
  Holes: x = None
  H.A.: None

Where is there a hole on the graph of the function?

• x = 2

• x = -2

• There are no holes.

• x = 5

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: x = -3;

  VA: x = 1

• Holes: x = -3, 1

  VA: None

• Holes: x = 1

  VA: x = -3

State the vertical asymptote.

• x = -2/5

• x = -5/2

• x = -5

• x = 2

Select ALL the information that applies to the given rational function.

• Vertical Asymptote is x = 1

• No Holes

• Horizontal Asymptote is y = 0

• No Horizontal Asymptote

Consider the function: \frac{x^2+x-6}{x^2+6x-16} Determine the excluded values and classify each as a hole or asymptote. There is a hole at ​ (a)   There is an asymptote at ​ (b)  

Which statements are true for the given rational function. Select all that apply.

• The horizontal asymptote is at y = 0.

• There is a hole at (6, ¾ ).

• The vertical asymptote is at x = -2.

• The x and y intercepts are at the origin.

• The domain is all real numbers except -2.

Select ALL the information that applies to the given rational function.

• Vertical Asymptote is x = -3

• Hole at (1, -2)

• Horizontal Asymptote is y = 2

• No Horizontal Asymptote

• Vertical Asymptote is x = 3

Select ALL the information that applies to the given rational function.

• Vertical Asymptote is x = -4

• No Holes

• Horizontal Asymptote is y = -1/4

• No Horizontal Asymptote

• Vertical Asymptote is x = 4

• A

• B

• C

• D